# complex limits

Given that $z$ is a complex number of the form $z = a +b i$, where $a, \, b \in \mathbb{R}$, and $\overline{z}$ is its conjugate, what is $$\lim_{z \to 0} \frac{\left( \overline{z} \right)^2}{ z^2} =\text{?}$$

When I ask Sage to do this limit, it says it's 1. I am almost certain that's not right. Here's the Sage code:

`sage: z=var('z')

sage: assume(z,'complex')

sage: limit((conjugate(z))^2/z^2,z=0) `

My analysis leads to DNE, so I wonder if I am misusing Sage.